That's true for hand washed mugs. Running your coffee cup under the hot tap in the kitchen uses vastly more energy than making a paper one or cleaning batches of cups in an industrial dishwasher.

Best alternative is my coffee cup that I have black coffee (no milk or sugar) and I refill but never wash. Gradually the layer of coffee tar on the inside exchanges with the fresh coffee.

It's also pretty hygienic, nobody else ever borrows my mug, and nothing can live on the layer of caffeine sludge.